In this letter, we shed some light on the clarification of the role of entanglement and coherence on extractable work by providing a model-independent analysis for general QBs.
We present theorem 1 to emphasize that generating nonzero extractable work requires non-vanishing entanglement or coherence during the charging process.
By restricting to incoherent QBs, namely, only diagonal elements are involved, we prove an inverse relationship between the final extractable work and the battery-charger entanglement, see theorem 2.
For a general QB, inspired by Refs. [1]}, [2]}, we treat extractable work as a sum of incoherent (extractable) work and coherent (extractable) work.
We show that the former is limited by the diagonal entropy of the battery, i.e., the sum of entanglement and coherence,
while the latter is promoted by the battery's coherence.
Furthermore, we argue that achieving maximally coherent work is fast than achieving maximally incoherent work.
We illustrate our results in some concrete models: the CS battery, the TC battery, and the \(XXZ\)  battery.
These results hold regardless of using free energy work or ergotropy as the quantifier of extractable work.
Our work deepens the understanding of the role of quantum resources played in energy transfer and work extraction.
